Properties

Label 1089.1.s.b.481.1
Level $1089$
Weight $1$
Character 1089.481
Analytic conductor $0.543$
Analytic rank $0$
Dimension $16$
Projective image $S_{4}$
CM/RM no
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1089,1,Mod(40,1089)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1089, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 21]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1089.40");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1089.s (of order \(30\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.543481798757\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{30})\)
Coefficient field: 16.0.26873856000000000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 2x^{14} - 8x^{10} - 16x^{8} - 32x^{6} + 128x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(S_{4}\)
Projective field: Galois closure of 4.2.107811.1

Embedding invariants

Embedding label 481.1
Root \(-0.575212 + 1.29195i\) of defining polynomial
Character \(\chi\) \(=\) 1089.481
Dual form 1089.1.s.b.403.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.575212 + 1.29195i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.669131 - 0.743145i) q^{4} +(-0.913545 + 0.406737i) q^{5} +(-0.831254 + 1.14412i) q^{6} +(0.294032 + 1.38331i) q^{7} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\) \(q+(-0.575212 + 1.29195i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.669131 - 0.743145i) q^{4} +(-0.913545 + 0.406737i) q^{5} +(-0.831254 + 1.14412i) q^{6} +(0.294032 + 1.38331i) q^{7} +(0.913545 + 0.406737i) q^{9} -1.41421i q^{10} +(-0.500000 - 0.866025i) q^{12} +(-1.95630 - 0.415823i) q^{14} +(-0.978148 + 0.207912i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-1.05097 + 0.946294i) q^{18} +(0.913545 + 0.406737i) q^{20} +1.41421i q^{21} +(0.809017 + 0.587785i) q^{27} +(0.831254 - 1.14412i) q^{28} +(-0.294032 - 1.38331i) q^{29} +(0.294032 - 1.38331i) q^{30} +(-0.104528 - 0.994522i) q^{31} +(1.22474 + 0.707107i) q^{32} +(-0.831254 - 1.14412i) q^{35} +(-0.309017 - 0.951057i) q^{36} +(-0.309017 + 0.951057i) q^{37} +(-1.82709 - 0.813473i) q^{42} -1.00000 q^{45} +(-0.669131 + 0.743145i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.913545 + 0.406737i) q^{49} +(-0.809017 + 0.587785i) q^{53} +(-1.22474 + 0.707107i) q^{54} +(1.95630 + 0.415823i) q^{58} +(0.669131 + 0.743145i) q^{59} +(0.809017 + 0.587785i) q^{60} +(1.40647 + 0.147826i) q^{61} +(1.34500 + 0.437016i) q^{62} +(-0.294032 + 1.38331i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.500000 - 0.866025i) q^{67} +(1.95630 - 0.415823i) q^{70} +(0.809017 + 0.587785i) q^{71} +(-1.34500 - 0.437016i) q^{73} +(-1.05097 - 0.946294i) q^{74} +(0.309017 + 0.951057i) q^{80} +(0.669131 + 0.743145i) q^{81} +(1.40647 + 0.147826i) q^{83} +(1.05097 - 0.946294i) q^{84} -1.41421i q^{87} +(0.575212 - 1.29195i) q^{90} +(0.104528 - 0.994522i) q^{93} +(-0.575212 - 1.29195i) q^{94} +(1.05097 + 0.946294i) q^{96} +(0.913545 + 0.406737i) q^{97} -1.41421i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{9} - 8 q^{12} + 4 q^{14} + 2 q^{15} - 2 q^{16} + 2 q^{20} + 4 q^{27} + 2 q^{31} + 4 q^{36} + 4 q^{37} - 4 q^{42} - 16 q^{45} - 2 q^{47} - 4 q^{48} - 2 q^{49} - 4 q^{53} - 4 q^{58} + 2 q^{59} + 4 q^{60} - 4 q^{64} + 8 q^{67} - 4 q^{70} + 4 q^{71} - 4 q^{80} + 2 q^{81} - 2 q^{93} + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(848\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.575212 + 1.29195i −0.575212 + 1.29195i 0.358368 + 0.933580i \(0.383333\pi\)
−0.933580 + 0.358368i \(0.883333\pi\)
\(3\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(4\) −0.669131 0.743145i −0.669131 0.743145i
\(5\) −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i \(-0.800000\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(6\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(7\) 0.294032 + 1.38331i 0.294032 + 1.38331i 0.838671 + 0.544639i \(0.183333\pi\)
−0.544639 + 0.838671i \(0.683333\pi\)
\(8\) 0 0
\(9\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(10\) 1.41421i 1.41421i
\(11\) 0 0
\(12\) −0.500000 0.866025i −0.500000 0.866025i
\(13\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(14\) −1.95630 0.415823i −1.95630 0.415823i
\(15\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(16\) 0.104528 0.994522i 0.104528 0.994522i
\(17\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(18\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(19\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(20\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(21\) 1.41421i 1.41421i
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(28\) 0.831254 1.14412i 0.831254 1.14412i
\(29\) −0.294032 1.38331i −0.294032 1.38331i −0.838671 0.544639i \(-0.816667\pi\)
0.544639 0.838671i \(-0.316667\pi\)
\(30\) 0.294032 1.38331i 0.294032 1.38331i
\(31\) −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i \(-0.866667\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(32\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(33\) 0 0
\(34\) 0 0
\(35\) −0.831254 1.14412i −0.831254 1.14412i
\(36\) −0.309017 0.951057i −0.309017 0.951057i
\(37\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(42\) −1.82709 0.813473i −1.82709 0.813473i
\(43\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 0 0
\(45\) −1.00000 −1.00000
\(46\) 0 0
\(47\) −0.669131 + 0.743145i −0.669131 + 0.743145i −0.978148 0.207912i \(-0.933333\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(48\) 0.309017 0.951057i 0.309017 0.951057i
\(49\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(54\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 1.95630 + 0.415823i 1.95630 + 0.415823i
\(59\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(60\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(61\) 1.40647 + 0.147826i 1.40647 + 0.147826i 0.777146 0.629320i \(-0.216667\pi\)
0.629320 + 0.777146i \(0.283333\pi\)
\(62\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(63\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(64\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.95630 0.415823i 1.95630 0.415823i
\(71\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(72\) 0 0
\(73\) −1.34500 0.437016i −1.34500 0.437016i −0.453990 0.891007i \(-0.650000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(74\) −1.05097 0.946294i −1.05097 0.946294i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(80\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(81\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(82\) 0 0
\(83\) 1.40647 + 0.147826i 1.40647 + 0.147826i 0.777146 0.629320i \(-0.216667\pi\)
0.629320 + 0.777146i \(0.283333\pi\)
\(84\) 1.05097 0.946294i 1.05097 0.946294i
\(85\) 0 0
\(86\) 0 0
\(87\) 1.41421i 1.41421i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0.575212 1.29195i 0.575212 1.29195i
\(91\) 0 0
\(92\) 0 0
\(93\) 0.104528 0.994522i 0.104528 0.994522i
\(94\) −0.575212 1.29195i −0.575212 1.29195i
\(95\) 0 0
\(96\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(97\) 0.913545 + 0.406737i 0.913545 + 0.406737i 0.809017 0.587785i \(-0.200000\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(98\) 1.41421i 1.41421i
\(99\) 0 0
\(100\) 0 0
\(101\) 0.575212 1.29195i 0.575212 1.29195i −0.358368 0.933580i \(-0.616667\pi\)
0.933580 0.358368i \(-0.116667\pi\)
\(102\) 0 0
\(103\) −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i \(-0.400000\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(104\) 0 0
\(105\) −0.575212 1.29195i −0.575212 1.29195i
\(106\) −0.294032 1.38331i −0.294032 1.38331i
\(107\) 1.34500 0.437016i 1.34500 0.437016i 0.453990 0.891007i \(-0.350000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(108\) −0.104528 0.994522i −0.104528 0.994522i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(112\) 1.40647 0.147826i 1.40647 0.147826i
\(113\) 0.978148 + 0.207912i 0.978148 + 0.207912i 0.669131 0.743145i \(-0.266667\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(117\) 0 0
\(118\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(123\) 0 0
\(124\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(125\) 0.309017 0.951057i 0.309017 0.951057i
\(126\) −1.61803 1.17557i −1.61803 1.17557i
\(127\) −0.831254 + 1.14412i −0.831254 + 1.14412i 0.156434 + 0.987688i \(0.450000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.831254 + 1.14412i 0.831254 + 1.14412i
\(135\) −0.978148 0.207912i −0.978148 0.207912i
\(136\) 0 0
\(137\) 0.104528 0.994522i 0.104528 0.994522i −0.809017 0.587785i \(-0.800000\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(138\) 0 0
\(139\) 1.05097 0.946294i 1.05097 0.946294i 0.0523360 0.998630i \(-0.483333\pi\)
0.998630 + 0.0523360i \(0.0166667\pi\)
\(140\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(141\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(142\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(143\) 0 0
\(144\) 0.500000 0.866025i 0.500000 0.866025i
\(145\) 0.831254 + 1.14412i 0.831254 + 1.14412i
\(146\) 1.33826 1.48629i 1.33826 1.48629i
\(147\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(148\) 0.913545 0.406737i 0.913545 0.406737i
\(149\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(150\) 0 0
\(151\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(156\) 0 0
\(157\) −0.978148 0.207912i −0.978148 0.207912i −0.309017 0.951057i \(-0.600000\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(158\) 0 0
\(159\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(160\) −1.40647 0.147826i −1.40647 0.147826i
\(161\) 0 0
\(162\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(163\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(167\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(168\) 0 0
\(169\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(174\) 1.82709 + 0.813473i 1.82709 + 0.813473i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(178\) 0 0
\(179\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(180\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(181\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(182\) 0 0
\(183\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(184\) 0 0
\(185\) −0.104528 0.994522i −0.104528 0.994522i
\(186\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(187\) 0 0
\(188\) 1.00000 1.00000
\(189\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(190\) 0 0
\(191\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(192\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(193\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(194\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(195\) 0 0
\(196\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(197\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 0 0
\(201\) 0.669131 0.743145i 0.669131 0.743145i
\(202\) 1.33826 + 1.48629i 1.33826 + 1.48629i
\(203\) 1.82709 0.813473i 1.82709 0.813473i
\(204\) 0 0
\(205\) 0 0
\(206\) 1.34500 0.437016i 1.34500 0.437016i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 2.00000 2.00000
\(211\) −1.40647 + 0.147826i −1.40647 + 0.147826i −0.777146 0.629320i \(-0.783333\pi\)
−0.629320 + 0.777146i \(0.716667\pi\)
\(212\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(213\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(214\) −0.209057 + 1.98904i −0.209057 + 1.98904i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.34500 0.437016i 1.34500 0.437016i
\(218\) 0 0
\(219\) −1.22474 0.707107i −1.22474 0.707107i
\(220\) 0 0
\(221\) 0 0
\(222\) −0.831254 1.14412i −0.831254 1.14412i
\(223\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(224\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(225\) 0 0
\(226\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(227\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(228\) 0 0
\(229\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.831254 + 1.14412i 0.831254 + 1.14412i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(234\) 0 0
\(235\) 0.309017 0.951057i 0.309017 0.951057i
\(236\) 0.104528 0.994522i 0.104528 0.994522i
\(237\) 0 0
\(238\) 0 0
\(239\) −0.294032 + 1.38331i −0.294032 + 1.38331i 0.544639 + 0.838671i \(0.316667\pi\)
−0.838671 + 0.544639i \(0.816667\pi\)
\(240\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(244\) −0.831254 1.14412i −0.831254 1.14412i
\(245\) 0.669131 0.743145i 0.669131 0.743145i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(250\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(251\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(252\) 1.22474 0.707107i 1.22474 0.707107i
\(253\) 0 0
\(254\) −1.00000 1.73205i −1.00000 1.73205i
\(255\) 0 0
\(256\) −0.978148 0.207912i −0.978148 0.207912i
\(257\) −1.33826 1.48629i −1.33826 1.48629i −0.669131 0.743145i \(-0.733333\pi\)
−0.669131 0.743145i \(-0.733333\pi\)
\(258\) 0 0
\(259\) −1.40647 0.147826i −1.40647 0.147826i
\(260\) 0 0
\(261\) 0.294032 1.38331i 0.294032 1.38331i
\(262\) 0 0
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) 0.500000 0.866025i 0.500000 0.866025i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(269\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(270\) 0.831254 1.14412i 0.831254 1.14412i
\(271\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(278\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(279\) 0.309017 0.951057i 0.309017 0.951057i
\(280\) 0 0
\(281\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(282\) −0.294032 1.38331i −0.294032 1.38331i
\(283\) 0.294032 1.38331i 0.294032 1.38331i −0.544639 0.838671i \(-0.683333\pi\)
0.838671 0.544639i \(-0.183333\pi\)
\(284\) −0.104528 0.994522i −0.104528 0.994522i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.831254 + 1.14412i 0.831254 + 1.14412i
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) −1.95630 + 0.415823i −1.95630 + 0.415823i
\(291\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(292\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(293\) −1.05097 + 0.946294i −1.05097 + 0.946294i −0.998630 0.0523360i \(-0.983333\pi\)
−0.0523360 + 0.998630i \(0.516667\pi\)
\(294\) 0.294032 1.38331i 0.294032 1.38331i
\(295\) −0.913545 0.406737i −0.913545 0.406737i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0.831254 1.14412i 0.831254 1.14412i
\(304\) 0 0
\(305\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.500000 0.866025i −0.500000 0.866025i
\(310\) −1.40647 + 0.147826i −1.40647 + 0.147826i
\(311\) −0.978148 0.207912i −0.978148 0.207912i −0.309017 0.951057i \(-0.600000\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(312\) 0 0
\(313\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(314\) 0.831254 1.14412i 0.831254 1.14412i
\(315\) −0.294032 1.38331i −0.294032 1.38331i
\(316\) 0 0
\(317\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(318\) 1.41421i 1.41421i
\(319\) 0 0
\(320\) 0.500000 0.866025i 0.500000 0.866025i
\(321\) 1.40647 0.147826i 1.40647 0.147826i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.104528 0.994522i 0.104528 0.994522i
\(325\) 0 0
\(326\) 0.294032 + 1.38331i 0.294032 + 1.38331i
\(327\) 0 0
\(328\) 0 0
\(329\) −1.22474 0.707107i −1.22474 0.707107i
\(330\) 0 0
\(331\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(332\) −0.831254 1.14412i −0.831254 1.14412i
\(333\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(334\) 0 0
\(335\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(336\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(337\) −1.05097 + 0.946294i −1.05097 + 0.946294i −0.998630 0.0523360i \(-0.983333\pi\)
−0.0523360 + 0.998630i \(0.516667\pi\)
\(338\) 0.294032 1.38331i 0.294032 1.38331i
\(339\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.575212 1.29195i −0.575212 1.29195i −0.933580 0.358368i \(-0.883333\pi\)
0.358368 0.933580i \(-0.383333\pi\)
\(348\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(349\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) −1.40647 + 0.147826i −1.40647 + 0.147826i
\(355\) −0.978148 0.207912i −0.978148 0.207912i
\(356\) 0 0
\(357\) 0 0
\(358\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(359\) −1.34500 0.437016i −1.34500 0.437016i −0.453990 0.891007i \(-0.650000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(360\) 0 0
\(361\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(362\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.40647 0.147826i 1.40647 0.147826i
\(366\) −1.33826 + 1.48629i −1.33826 + 1.48629i
\(367\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(371\) −1.05097 0.946294i −1.05097 0.946294i
\(372\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) 0.500000 0.866025i 0.500000 0.866025i
\(376\) 0 0
\(377\) 0 0
\(378\) −1.33826 1.48629i −1.33826 1.48629i
\(379\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(380\) 0 0
\(381\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(382\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(383\) −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i \(-0.866667\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.309017 0.951057i −0.309017 0.951057i
\(389\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −1.82709 0.813473i −1.82709 0.813473i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0.575212 1.29195i 0.575212 1.29195i
\(399\) 0 0
\(400\) 0 0
\(401\) −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i \(-0.800000\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(402\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(403\) 0 0
\(404\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(405\) −0.913545 0.406737i −0.913545 0.406737i
\(406\) 2.82843i 2.82843i
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(410\) 0 0
\(411\) 0.309017 0.951057i 0.309017 0.951057i
\(412\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(413\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(414\) 0 0
\(415\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(416\) 0 0
\(417\) 1.22474 0.707107i 1.22474 0.707107i
\(418\) 0 0
\(419\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(420\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(421\) 0.669131 0.743145i 0.669131 0.743145i −0.309017 0.951057i \(-0.600000\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(422\) 0.618034 1.90211i 0.618034 1.90211i
\(423\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(424\) 0 0
\(425\) 0 0
\(426\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(427\) 0.209057 + 1.98904i 0.209057 + 1.98904i
\(428\) −1.22474 0.707107i −1.22474 0.707107i
\(429\) 0 0
\(430\) 0 0
\(431\) −0.831254 1.14412i −0.831254 1.14412i −0.987688 0.156434i \(-0.950000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(432\) 0.669131 0.743145i 0.669131 0.743145i
\(433\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(434\) −0.209057 + 1.98904i −0.209057 + 1.98904i
\(435\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(436\) 0 0
\(437\) 0 0
\(438\) 1.61803 1.17557i 1.61803 1.17557i
\(439\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) 0.669131 0.743145i 0.669131 0.743145i −0.309017 0.951057i \(-0.600000\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(444\) 0.978148 0.207912i 0.978148 0.207912i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.05097 0.946294i −1.05097 0.946294i
\(449\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.500000 0.866025i −0.500000 0.866025i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.40647 + 0.147826i 1.40647 + 0.147826i 0.777146 0.629320i \(-0.216667\pi\)
0.629320 + 0.777146i \(0.283333\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(462\) 0 0
\(463\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(464\) −1.40647 + 0.147826i −1.40647 + 0.147826i
\(465\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(466\) −1.95630 + 0.415823i −1.95630 + 0.415823i
\(467\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(468\) 0 0
\(469\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(470\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(471\) −0.913545 0.406737i −0.913545 0.406737i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(478\) −1.61803 1.17557i −1.61803 1.17557i
\(479\) −1.40647 0.147826i −1.40647 0.147826i −0.629320 0.777146i \(-0.716667\pi\)
−0.777146 + 0.629320i \(0.783333\pi\)
\(480\) −1.34500 0.437016i −1.34500 0.437016i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.00000 −1.00000
\(486\) −1.40647 + 0.147826i −1.40647 + 0.147826i
\(487\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(488\) 0 0
\(489\) 0.913545 0.406737i 0.913545 0.406737i
\(490\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(491\) 1.05097 0.946294i 1.05097 0.946294i 0.0523360 0.998630i \(-0.483333\pi\)
0.998630 + 0.0523360i \(0.0166667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(498\) −1.33826 + 1.48629i −1.33826 + 1.48629i
\(499\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(500\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(501\) 0 0
\(502\) 0 0
\(503\) 1.34500 0.437016i 1.34500 0.437016i 0.453990 0.891007i \(-0.350000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(504\) 0 0
\(505\) 1.41421i 1.41421i
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) 1.40647 0.147826i 1.40647 0.147826i
\(509\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(510\) 0 0
\(511\) 0.209057 1.98904i 0.209057 1.98904i
\(512\) 0.831254 1.14412i 0.831254 1.14412i
\(513\) 0 0
\(514\) 2.68999 0.874032i 2.68999 0.874032i
\(515\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(516\) 0 0
\(517\) 0 0
\(518\) 1.00000 1.73205i 1.00000 1.73205i
\(519\) 0 0
\(520\) 0 0
\(521\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(522\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(523\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(530\) 0.831254 + 1.14412i 0.831254 + 1.14412i
\(531\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(536\) 0 0
\(537\) −0.104528 0.994522i −0.104528 0.994522i
\(538\) 1.22474 0.707107i 1.22474 0.707107i
\(539\) 0 0
\(540\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(541\) −0.831254 1.14412i −0.831254 1.14412i −0.987688 0.156434i \(-0.950000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(542\) 0 0
\(543\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.05097 0.946294i −1.05097 0.946294i −0.0523360 0.998630i \(-0.516667\pi\)
−0.998630 + 0.0523360i \(0.983333\pi\)
\(548\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(549\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.104528 0.994522i 0.104528 0.994522i
\(556\) −1.40647 0.147826i −1.40647 0.147826i
\(557\) 1.34500 + 0.437016i 1.34500 + 0.437016i 0.891007 0.453990i \(-0.150000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(558\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(559\) 0 0
\(560\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(564\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(565\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(566\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(567\) −0.831254 + 1.14412i −0.831254 + 1.14412i
\(568\) 0 0
\(569\) 1.05097 + 0.946294i 1.05097 + 0.946294i 0.998630 0.0523360i \(-0.0166667\pi\)
0.0523360 + 0.998630i \(0.483333\pi\)
\(570\) 0 0
\(571\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(572\) 0 0
\(573\) 1.00000 1.00000
\(574\) 0 0
\(575\) 0 0
\(576\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(577\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(578\) −1.40647 0.147826i −1.40647 0.147826i
\(579\) 0 0
\(580\) 0.294032 1.38331i 0.294032 1.38331i
\(581\) 0.209057 + 1.98904i 0.209057 + 1.98904i
\(582\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −0.618034 1.90211i −0.618034 1.90211i
\(587\) −0.978148 + 0.207912i −0.978148 + 0.207912i −0.669131 0.743145i \(-0.733333\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(588\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(589\) 0 0
\(590\) 1.05097 0.946294i 1.05097 0.946294i
\(591\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(592\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(593\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.978148 0.207912i −0.978148 0.207912i
\(598\) 0 0
\(599\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(600\) 0 0
\(601\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(602\) 0 0
\(603\) 0.809017 0.587785i 0.809017 0.587785i
\(604\) 0 0
\(605\) 0 0
\(606\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(607\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(608\) 0 0
\(609\) 1.95630 0.415823i 1.95630 0.415823i
\(610\) 0.209057 1.98904i 0.209057 1.98904i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(618\) 1.40647 0.147826i 1.40647 0.147826i
\(619\) 0.669131 0.743145i 0.669131 0.743145i −0.309017 0.951057i \(-0.600000\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(620\) 0.309017 0.951057i 0.309017 0.951057i
\(621\) 0 0
\(622\) 0.831254 1.14412i 0.831254 1.14412i
\(623\) 0 0
\(624\) 0 0
\(625\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(629\) 0 0
\(630\) 1.95630 + 0.415823i 1.95630 + 0.415823i
\(631\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(632\) 0 0
\(633\) −1.40647 0.147826i −1.40647 0.147826i
\(634\) 0 0
\(635\) 0.294032 1.38331i 0.294032 1.38331i
\(636\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(637\) 0 0
\(638\) 0 0
\(639\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(640\) 0 0
\(641\) −1.33826 + 1.48629i −1.33826 + 1.48629i −0.669131 + 0.743145i \(0.733333\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(642\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(643\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 1.40647 0.147826i 1.40647 0.147826i
\(652\) −0.978148 0.207912i −0.978148 0.207912i
\(653\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.05097 0.946294i −1.05097 0.946294i
\(658\) 1.61803 1.17557i 1.61803 1.17557i
\(659\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(662\) 1.40647 0.147826i 1.40647 0.147826i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.575212 1.29195i −0.575212 1.29195i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) −1.22474 0.707107i −1.22474 0.707107i
\(671\) 0 0
\(672\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(673\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(674\) −0.618034 1.90211i −0.618034 1.90211i
\(675\) 0 0
\(676\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(677\) −1.40647 0.147826i −1.40647 0.147826i −0.629320 0.777146i \(-0.716667\pi\)
−0.777146 + 0.629320i \(0.783333\pi\)
\(678\) −1.05097 + 0.946294i −1.05097 + 0.946294i
\(679\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) 0 0
\(685\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i \(-0.533333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 2.00000 2.00000
\(695\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(700\) 0 0
\(701\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.500000 0.866025i 0.500000 0.866025i
\(706\) 0 0
\(707\) 1.95630 + 0.415823i 1.95630 + 0.415823i
\(708\) 0.309017 0.951057i 0.309017 0.951057i
\(709\) −0.104528 + 0.994522i −0.104528 + 0.994522i 0.809017 + 0.587785i \(0.200000\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(710\) 0.831254 1.14412i 0.831254 1.14412i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(717\) −0.575212 + 1.29195i −0.575212 + 1.29195i
\(718\) 1.33826 1.48629i 1.33826 1.48629i
\(719\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(720\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(721\) 0.831254 1.14412i 0.831254 1.14412i
\(722\) −0.294032 1.38331i −0.294032 1.38331i
\(723\) 0 0
\(724\) −0.104528 0.994522i −0.104528 0.994522i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(730\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(731\) 0 0
\(732\) −0.575212 1.29195i −0.575212 1.29195i
\(733\) 1.05097 0.946294i 1.05097 0.946294i 0.0523360 0.998630i \(-0.483333\pi\)
0.998630 + 0.0523360i \(0.0166667\pi\)
\(734\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(735\) 0.809017 0.587785i 0.809017 0.587785i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(740\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(741\) 0 0
\(742\) 1.82709 0.813473i 1.82709 0.813473i
\(743\) −0.575212 1.29195i −0.575212 1.29195i −0.933580 0.358368i \(-0.883333\pi\)
0.358368 0.933580i \(-0.383333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(748\) 0 0
\(749\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(750\) 0.831254 + 1.14412i 0.831254 + 1.14412i
\(751\) 0.978148 + 0.207912i 0.978148 + 0.207912i 0.669131 0.743145i \(-0.266667\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.34500 0.437016i 1.34500 0.437016i
\(757\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.40647 + 0.147826i −1.40647 + 0.147826i −0.777146 0.629320i \(-0.783333\pi\)
−0.629320 + 0.777146i \(0.716667\pi\)
\(762\) −0.618034 1.90211i −0.618034 1.90211i
\(763\) 0 0
\(764\) −0.809017 0.587785i −0.809017 0.587785i
\(765\) 0 0
\(766\) 1.34500 + 0.437016i 1.34500 + 0.437016i
\(767\) 0 0
\(768\) −0.913545 0.406737i −0.913545 0.406737i
\(769\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(770\) 0 0
\(771\) −1.00000 1.73205i −1.00000 1.73205i
\(772\) 0 0
\(773\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.34500 0.437016i −1.34500 0.437016i
\(778\) −0.294032 + 1.38331i −0.294032 + 1.38331i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.575212 1.29195i 0.575212 1.29195i
\(784\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(785\) 0.978148 0.207912i 0.978148 0.207912i
\(786\) 0 0
\(787\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(788\) 1.05097 0.946294i 1.05097 0.946294i
\(789\) 0 0
\(790\) 0 0
\(791\) 1.41421i 1.41421i
\(792\) 0 0
\(793\) 0 0
\(794\) 0.575212 1.29195i 0.575212 1.29195i
\(795\) 0.669131 0.743145i 0.669131 0.743145i
\(796\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(797\) −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i \(-0.800000\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 1.41421i 1.41421i
\(803\) 0 0
\(804\) −1.00000 −1.00000
\(805\) 0 0
\(806\) 0 0
\(807\) −0.669131 0.743145i −0.669131 0.743145i
\(808\) 0 0
\(809\) −0.831254 + 1.14412i −0.831254 + 1.14412i 0.156434 + 0.987688i \(0.450000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(810\) 1.05097 0.946294i 1.05097 0.946294i
\(811\) −1.34500 + 0.437016i −1.34500 + 0.437016i −0.891007 0.453990i \(-0.850000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(812\) −1.82709 0.813473i −1.82709 0.813473i
\(813\) 0 0
\(814\) 0 0
\(815\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(822\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(823\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −1.00000 1.73205i −1.00000 1.73205i
\(827\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(828\) 0 0
\(829\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(830\) 0.209057 1.98904i 0.209057 1.98904i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0.209057 + 1.98904i 0.209057 + 1.98904i
\(835\) 0 0
\(836\) 0 0
\(837\) 0.500000 0.866025i 0.500000 0.866025i
\(838\) 0.831254 + 1.14412i 0.831254 + 1.14412i
\(839\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(840\) 0 0
\(841\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(842\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(843\) 0 0
\(844\) 1.05097 + 0.946294i 1.05097 + 0.946294i
\(845\) 0.809017 0.587785i 0.809017 0.587785i
\(846\) 1.41421i 1.41421i
\(847\) 0 0
\(848\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(849\) 0.575212 1.29195i 0.575212 1.29195i
\(850\) 0 0
\(851\) 0 0
\(852\) 0.104528 0.994522i 0.104528 0.994522i
\(853\) −1.40647 0.147826i −1.40647 0.147826i −0.629320 0.777146i \(-0.716667\pi\)
−0.777146 + 0.629320i \(0.783333\pi\)
\(854\) −2.68999 0.874032i −2.68999 0.874032i
\(855\) 0 0
\(856\) 0 0
\(857\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(858\) 0 0
\(859\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.95630 0.415823i 1.95630 0.415823i
\(863\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(864\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(865\) 0 0
\(866\) 0 0
\(867\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(868\) −1.22474 0.707107i −1.22474 0.707107i
\(869\) 0 0
\(870\) −2.00000 −2.00000
\(871\) 0 0
\(872\) 0 0
\(873\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(874\) 0 0
\(875\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(876\) 0.294032 + 1.38331i 0.294032 + 1.38331i
\(877\) −0.294032 + 1.38331i −0.294032 + 1.38331i 0.544639 + 0.838671i \(0.316667\pi\)
−0.838671 + 0.544639i \(0.816667\pi\)
\(878\) 0.209057 + 1.98904i 0.209057 + 1.98904i
\(879\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(880\) 0 0
\(881\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) 0.575212 1.29195i 0.575212 1.29195i
\(883\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(884\) 0 0
\(885\) −0.809017 0.587785i −0.809017 0.587785i
\(886\) 0.575212 + 1.29195i 0.575212 + 1.29195i
\(887\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(888\) 0 0
\(889\) −1.82709 0.813473i −1.82709 0.813473i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(896\) 0 0
\(897\) 0 0
\(898\) −0.294032 1.38331i −0.294032 1.38331i
\(899\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −0.978148 0.207912i −0.978148 0.207912i
\(906\) 0 0
\(907\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(908\) 0 0
\(909\) 1.05097 0.946294i 1.05097 0.946294i
\(910\) 0 0
\(911\) −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i \(-0.533333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(915\) −1.40647 + 0.147826i −1.40647 + 0.147826i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.209057 + 1.98904i 0.209057 + 1.98904i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −0.309017 0.951057i −0.309017 0.951057i
\(928\) 0.618034 1.90211i 0.618034 1.90211i
\(929\) 0.104528 0.994522i 0.104528 0.994522i −0.809017 0.587785i \(-0.800000\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(930\) −1.40647 0.147826i −1.40647 0.147826i
\(931\) 0 0
\(932\) 0.294032 1.38331i 0.294032 1.38331i
\(933\) −0.913545 0.406737i −0.913545 0.406737i
\(934\) 1.22474 0.707107i 1.22474 0.707107i
\(935\) 0 0
\(936\) 0 0
\(937\) −0.831254 1.14412i −0.831254 1.14412i −0.987688 0.156434i \(-0.950000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(938\) −1.33826 + 1.48629i −1.33826 + 1.48629i
\(939\) 0 0
\(940\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(941\) 0.575212 + 1.29195i 0.575212 + 1.29195i 0.933580 + 0.358368i \(0.116667\pi\)
−0.358368 + 0.933580i \(0.616667\pi\)
\(942\) 1.05097 0.946294i 1.05097 0.946294i
\(943\) 0 0
\(944\) 0.809017 0.587785i 0.809017 0.587785i
\(945\) 1.41421i 1.41421i
\(946\) 0 0
\(947\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.34500 + 0.437016i 1.34500 + 0.437016i 0.891007 0.453990i \(-0.150000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(954\) 0.294032 1.38331i 0.294032 1.38331i
\(955\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(956\) 1.22474 0.707107i 1.22474 0.707107i
\(957\) 0 0
\(958\) 1.00000 1.73205i 1.00000 1.73205i
\(959\) 1.40647 0.147826i 1.40647 0.147826i
\(960\) 0.669131 0.743145i 0.669131 0.743145i
\(961\) 0 0
\(962\) 0 0
\(963\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0.575212 1.29195i 0.575212 1.29195i
\(971\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(972\) 0.309017 0.951057i 0.309017 0.951057i
\(973\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(974\) 1.40647 + 0.147826i 1.40647 + 0.147826i
\(975\) 0 0
\(976\) 0.294032 1.38331i 0.294032 1.38331i
\(977\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(978\) 1.41421i 1.41421i
\(979\) 0 0
\(980\) −1.00000 −1.00000
\(981\) 0 0
\(982\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(983\) −0.978148 + 0.207912i −0.978148 + 0.207912i −0.669131 0.743145i \(-0.733333\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(984\) 0 0
\(985\) −0.575212 1.29195i −0.575212 1.29195i
\(986\) 0 0
\(987\) −1.05097 0.946294i −1.05097 0.946294i
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0.575212 1.29195i 0.575212 1.29195i
\(993\) −0.309017 0.951057i −0.309017 0.951057i
\(994\) −1.33826 1.48629i −1.33826 1.48629i
\(995\) 0.913545 0.406737i 0.913545 0.406737i
\(996\) −0.575212 1.29195i −0.575212 1.29195i
\(997\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(998\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(999\) −0.809017 + 0.587785i −0.809017 + 0.587785i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1089.1.s.b.481.1 16
3.2 odd 2 3267.1.w.b.118.2 16
9.2 odd 6 3267.1.w.b.1207.1 16
9.7 even 3 inner 1089.1.s.b.844.2 16
11.2 odd 10 1089.1.h.a.967.1 yes 4
11.3 even 5 inner 1089.1.s.b.94.2 16
11.4 even 5 inner 1089.1.s.b.40.1 16
11.5 even 5 inner 1089.1.s.b.112.1 16
11.6 odd 10 inner 1089.1.s.b.112.2 16
11.7 odd 10 inner 1089.1.s.b.40.2 16
11.8 odd 10 inner 1089.1.s.b.94.1 16
11.9 even 5 1089.1.h.a.967.2 yes 4
11.10 odd 2 inner 1089.1.s.b.481.2 16
33.2 even 10 3267.1.h.a.604.2 4
33.5 odd 10 3267.1.w.b.1927.2 16
33.8 even 10 3267.1.w.b.820.2 16
33.14 odd 10 3267.1.w.b.820.1 16
33.17 even 10 3267.1.w.b.1927.1 16
33.20 odd 10 3267.1.h.a.604.1 4
33.26 odd 10 3267.1.w.b.766.2 16
33.29 even 10 3267.1.w.b.766.1 16
33.32 even 2 3267.1.w.b.118.1 16
99.2 even 30 3267.1.h.a.1693.1 4
99.7 odd 30 inner 1089.1.s.b.403.1 16
99.16 even 15 inner 1089.1.s.b.475.1 16
99.20 odd 30 3267.1.h.a.1693.2 4
99.25 even 15 inner 1089.1.s.b.457.2 16
99.29 even 30 3267.1.w.b.1855.2 16
99.38 odd 30 3267.1.w.b.3016.2 16
99.43 odd 6 inner 1089.1.s.b.844.1 16
99.47 odd 30 3267.1.w.b.1909.1 16
99.52 odd 30 inner 1089.1.s.b.457.1 16
99.61 odd 30 inner 1089.1.s.b.475.2 16
99.65 even 6 3267.1.w.b.1207.2 16
99.70 even 15 inner 1089.1.s.b.403.2 16
99.74 even 30 3267.1.w.b.1909.2 16
99.79 odd 30 1089.1.h.a.241.2 yes 4
99.83 even 30 3267.1.w.b.3016.1 16
99.92 odd 30 3267.1.w.b.1855.1 16
99.97 even 15 1089.1.h.a.241.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1089.1.h.a.241.1 4 99.97 even 15
1089.1.h.a.241.2 yes 4 99.79 odd 30
1089.1.h.a.967.1 yes 4 11.2 odd 10
1089.1.h.a.967.2 yes 4 11.9 even 5
1089.1.s.b.40.1 16 11.4 even 5 inner
1089.1.s.b.40.2 16 11.7 odd 10 inner
1089.1.s.b.94.1 16 11.8 odd 10 inner
1089.1.s.b.94.2 16 11.3 even 5 inner
1089.1.s.b.112.1 16 11.5 even 5 inner
1089.1.s.b.112.2 16 11.6 odd 10 inner
1089.1.s.b.403.1 16 99.7 odd 30 inner
1089.1.s.b.403.2 16 99.70 even 15 inner
1089.1.s.b.457.1 16 99.52 odd 30 inner
1089.1.s.b.457.2 16 99.25 even 15 inner
1089.1.s.b.475.1 16 99.16 even 15 inner
1089.1.s.b.475.2 16 99.61 odd 30 inner
1089.1.s.b.481.1 16 1.1 even 1 trivial
1089.1.s.b.481.2 16 11.10 odd 2 inner
1089.1.s.b.844.1 16 99.43 odd 6 inner
1089.1.s.b.844.2 16 9.7 even 3 inner
3267.1.h.a.604.1 4 33.20 odd 10
3267.1.h.a.604.2 4 33.2 even 10
3267.1.h.a.1693.1 4 99.2 even 30
3267.1.h.a.1693.2 4 99.20 odd 30
3267.1.w.b.118.1 16 33.32 even 2
3267.1.w.b.118.2 16 3.2 odd 2
3267.1.w.b.766.1 16 33.29 even 10
3267.1.w.b.766.2 16 33.26 odd 10
3267.1.w.b.820.1 16 33.14 odd 10
3267.1.w.b.820.2 16 33.8 even 10
3267.1.w.b.1207.1 16 9.2 odd 6
3267.1.w.b.1207.2 16 99.65 even 6
3267.1.w.b.1855.1 16 99.92 odd 30
3267.1.w.b.1855.2 16 99.29 even 30
3267.1.w.b.1909.1 16 99.47 odd 30
3267.1.w.b.1909.2 16 99.74 even 30
3267.1.w.b.1927.1 16 33.17 even 10
3267.1.w.b.1927.2 16 33.5 odd 10
3267.1.w.b.3016.1 16 99.83 even 30
3267.1.w.b.3016.2 16 99.38 odd 30